ABSTRACT
In Chapter 2, just after proving Proposition 2.3, we gave a cunning geometrical construction that demonstrated the existence of the real number n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315382517/471f85d9-9517-49b3-9a80-cddf80ac5607/content/eq151.tif"/> for any positive integer n. However, proving the existence of a cube root and, more generally, an n th root of any positive real number x is much harder and requires a deeper analysis of the reals than we have undertaken thus far. We shall carry out such an analysis later, in Chapter 24. However, because we wish to include n th roots in the discussion of complex numbers in the next chapter, we pick out the main result from Chapter 24 on such matters, namely Proposition 24.2, and state it here. (It is, of course, proved in Chapter 24.)
